Convert all complex numbers to trigonometric form and then simplify the expression. Write the answer in standard form.? (2+2i)5(3+i)3(3+i)10

1 Answer
May 14, 2018

2734i274

Explanation:

So this took me so many attempts and here it goes:

Find the r values using this formula:

r=x2+y2

Plug in:

[22(cos45o+isin45o)]5[32(cos135o+isin135o)]3[2(cos30o+isin30o)]10

Power and Multiply:

(22)5 see how I powered the 22 and you do the same with the rest

(22)5(cos5×45o+isin5×45o)(32)3(cos3×135o+isin3×135o)210(cos10×+isin10×30)

Simplify:

1282(cos225o+isin225o)542(cos405o+isin405o)1024(cos300o+isin300o)

13824(cos630o+isin630o)1024(cos300o+isin300o)

Divide:

272 (cos630o300o+isin630o300o)

Simplify:

272 (cos330o+isin330o)

Which gives your answer . . .